Yes, but it's only part of it. The simplified diagram shows tele-centric focused light, and the micro-lens helps to concentrate the light on the photosensitive areas instead of the supporting structures. When the chief ray angle is oblique, then the angle is changed more in the perpendicular direction as well.

In practice, there can also be a sort of aperture mask (perhaps simplified by just the 'walls' in the diagram) near the top of the sensel structure, which will cast a 'shadow' when light enters at an angle, and the micro-lens will reduce that by reducing the angle of light to become more perpendicular. More importantly, when the micro-lens is not centered above the sensel but rather somewhat offset in the direction of the center of the sensor array, it can be even more effective when the refractive index is closely matched to the amount of offset.

The problem with the samples is not flange distance but lenses that are not calculated for digital sensors. Leica has the same issues, but they developed their own sensor with deeper wells and have bar codes on the lens that tell the camera about the lens they use and approximate aperture using a light metering trick.

The difference between the A7 and A7r is probably coming from the pixels being smaller on the A7r.

This has nothing to do with short flange distance nor to offset microlenses and a lot to do with distance of outlet pupil to sensor. Of course would the flange distance be significantly longer, they would not be able to viewfinder lenses on the camera, so problem would not arise. Leica R lenses, Canons, Nikons work just fine.

Someone posted the following comparison.Help yourself see how they perform.

Thanks for the examples. They are from lens designs made for film, not for digital sensors. Digital Leica cameras also have a problem with these lens designs, it would have been nice to see those as well (probably with even worse results than from the Sony's). Nothing to do with Sony (or Leica, or anybody else) in particular, just the wrong lens design for digital cameras.

Here you can see the optical design of the 21mm f/4 used in the sample images, a design for a very short flange to film distance with large negative lenses at the rear. Compare that to another 21mm design, with positive elements at the rear, and proven usability with digital sensors in general. The Voigtländer 21mm f/1.8 also performs well on digital sensors, its design has a number of positive lens elements at the rear.